On the total amount of resources occupied by serviced customers

Abstract

We consider a model of a multi-server queueing system with losses caused by lack of resources necessary to service claims. A claim accepted for servicing occupies a random amount of resources of several types with given distribution functions. Random vectors that define the requirements of claims for resources are independent of the processes of customer arrivals and servicing, mutually independent, and identically distributed. Under the assumptions of a Poisson arrival process and exponential service times, we analytically find the joint distribution of the number of customers in the system and the vector of amounts of resources occupied by them. We show sample computations that illustrate an application of the model to analyzing the characteristics of a videoconferencing service in an LTE wireless network.